Aberdeen ended the season with a win over Hearts but could not catch Hibs in the race for Uefa Cup football.
A header from Richie Byrne and a close range finish from Derek Adams earned the Dons the points but Hibs beat them to third place on goal difference.
With Hibs losing 1-0 to Rangers, Aberdeen needed to win by five goals and they created a number of chances.
Wave after wave of red shirts swept forward all afternoon but it wasn't to be for Jimmy Calderwood's side.
Knowing a six-goal swing was needed, the Dons started with three at the back and committed men into attack.
The home team began the game at a very high tempo but in their haste too many passes were wasted.
And their cavalier approach almost caught them out when Alexander Diamond's slip gave Dennis Wyness a clear sight of goal but the former Don pulled his shot wide.
Aberdeen went close when Byrne nodded the ball back for Phil McGuire who, in his final appearance for the Dons, smashed a volley off the woodwork.
Scott Muirhead then found Darren Mackie with a terrific low cross but the striker - despite beating keeper Craig Gordon to it - could only clip the ball wide.
Pittodrie sensed the opening goal was coming and it arrived on the stroke of half-time.
Scott Severin played a free-kick into the six-yard box for Byrne, who outjumped everyone to nod it beyond Gordon's despairing hand into the far corner.
Early in the second half Dons substitute Lubomir Blaha rose to head Severin's corner towards goal but just as he turned to celebrate, Adams nicked in and stole the glory.
The home support roared their favourites on when news of Nacho Novo's goal for Rangers filtered through to Pittodrie.
Aberdeen were cursing Gordon in the 77th minute when the Scotland international beat away Mackie's point-blank header.
And Gordon made another impressive stop to keep out Kevin McNaughton's header.
The home team kept pressing until the final minutes when the European dream vanished.
Aberdeen: Esson, McGuire (Blaha 45), Diamond, Heikkinen (Dempsey 71), Byrne, McNaughton, Severin, Clark, Muirhead, Mackie, Adams (Stewart 77). Subs Not Used: Preece, Winter, Considine, Macauley.
Booked: Mackie. Goals: Byrne 45, Adams 49.
Hearts: Gordon, Neilson, Webster, Sives (Tierney 78), Wallace, Mikoliunas (McGeown 65), Hartley, MacFarlane, Hamill, Wyness, Miller (Elliot 65). Subs Not Used: McDonald, Pelosi, Thomson, Driver.
Booked: Sives, Hartley.
Ref: I Fyfe